Polynomial Regression Calculator

What Is Polynomial Regression?

Polynomial regression fits a curved relationship between an independent variable $x$ and a dependent variable $y$ using a polynomial of chosen degree. Degree 1 is linear regression; higher degrees capture bends and peaks. See also the Linear Regression Calculator and Exponential Regression Calculator.

Polynomial Regression Equation

$$y = a_0 + a_1 x + a_2 x^2 + \cdots + a_n x^n$$

Coefficients are found by least squares: minimize the sum of squared residuals between observed and predicted $y$ values. You need at least $n + 1$ points to fit a degree-$n$ model.

Interpreting R²

The coefficient of determination $R^2$ measures how much variation in $y$ is explained by the polynomial model. Values closer to 1 indicate a better fit, but very high-degree models can overfit small datasets.